Defining objective functions for sensitivity analysis of interpolation parameters

@inproceedings{P202_Gerland,
 abstract = { The contribution of model parameter uncertainties to the global uncertainty of numerical simulations
is quantifiable thanks to sensitivity analysis methods. These widely implemented methods
require (1) an experimental design describing the set of possible values for the input parameter,
and (2) an objective function measuring the output of the numerical simulation. Whereas defining
an objective function is almost direct with process-based simulations, it is more difficult to express
the quality of a DSI or kriging estimation.
The main matter is now to find an objective function representing the quality of an interpolation,
to use in conjunction with visual quality control. However, several criteria may be used to judge
about the quality of some interpolation methods. In this work, we consider the artefacts some times
obtained around conditioning data points as indicator of bad interpolation parameters.
Therefore, we suggest two new criteria to evaluate and separate quality levels : one for isotropic
and the second for anisotropic interpolated surfaces. From [Caruso and Quarta, 1998], we adapted
the “roughness” criterion originally created to compare interpolation methods to a universel criterion
to evalute and quantify the quality of interpolation. By exention, we created a new criterion
to allow an evaluation of anisotropic interpolation, in order to be the most complete and accurate
in this evaluation. Eventually, we will be able to integrate this work to the sensitivity analysis of
partials parameters uncertainties inside global model uncertainty.
keywords : quality of interpolation, roughness, sensitivity analysis },
 author = { Sophie, Gerland AND Kedzierski, Pierre AND Caumon, Guillaume },
 booktitle = { Proc. 27th Gocad Meeting, Nancy },
 publisher = { ASGA },
 title = { Defining objective functions for sensitivity analysis of interpolation parameters },
 year = { 2007 }
}